Claudia I. Scheimbauer

research interests

My research area is mathematical physics. I work on fully extended topological field theories (in the sense of Lurie) using higher category theory, factorization algebras/homology, and derived symplectic geometry. I am also interested in open-closed field theories in the sense of Costello and Lurie and relative, or twisted, field theories in the sense of Freed-Teleman and Stolz-Teichner. Recently, I have become interested in questions revolving around objects carrying a higher categorical structure called "2-Segal object" which was introduced by Dyckerhoff-Kapranov and Gàlvez-Carrillo-Kock-Tonks and generalizes the idea of a categorical structure with a multivalued composition. These questions include applications in topology (Waldhausen construction and K-theory, configuration spaces) and mathematical physics (modular functors).

articles

in preparation

thesis

Factorization homology as a fully extended topological field theory

We first give a precise definition of a fully extended n-dimensional topological field theory using complete n-fold Segal spaces as a model for (∞,n)-categories and then, given an E_n-algebra A, we explicitly construct a fully extended TFT given by taking factorization homology with coefficients in A. This is the fully extended n-TFT corresponding (via the cobordism hypothesis) to the E_n-algebra A, which is a fully dualizable object in a suitable Morita-(∞,n)-category Alg_n of E_n -algebras.

Some notes from my talk at the Winter School in Mathematical Physics 2014 in Les Diablerets. A video of a talk I gave about my thesis is available here.

Here is the current version of my thesis on "Factorization Homology as a Fully Extended Topological Field Theory".

extended abstracts and slides